Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model

Abstract

In this study, the dynamics of elliptic membrane shell model has been proposed and discussed numerically for the first time. Firstly, we show that the solution of this model exists and is unique. Secondly, we consider spatial and time discretizations of the time-dependent elliptic membrane shell by finite element method and Newmark scheme, respectively. Then, the corresponding existence, uniqueness, stability, convergence and a priori error estimate are given. Finally, we present numerical results involving a portion of an ellipsoidal shell and a portion of a spherical shell to verify the efficiency and convergence of the numerical scheme.